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A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum. PACS number(s): 25.70. Ef,23.50.+z,25.60+v,21.60.Cs Typeset using REVT E X 1 The prospect of reaching and measuring very unstable nuclei, as is materializing now, opens the possibility of studying spectroscopic processes occuring in the continuum part of nuclear spectra. Much work has already been done in this subject, particularly regarding halo nuclei [1]. Still, the role played by single-particle resonances and of the continuum itself upon particles moving in the continuum of a heavy nucleus is not fully understood. For instance, one may wonder whether two particles outside a core where the Fermi level is immersed in the continuum may produce a quasibound state and, in this case, whether that state is built upon narrow single-particle resonances or by an interplay between the two-particle interaction and the continuum, or by a combination of these mechanisms, as it happens in typical halo nuclei. To answer such questions is a difficult undertaking, particularly because the resonances on the real energy axis do not correspond to a definite state. A way of approaching this problem is by solving the Schrödinger equation with outgoing boundary conditions. One thus obtains the resonances as poles of the S-matrix in the complex energy plane. These poles (Gamow resonances) can be considered discrete states on the same footing as bound states (see Ref.[2] and references therein). However, in this case one finds that physical quantities, like energies and probabilities, become complex. One may attempt to give meaning to these complex quantities. Thus, it is usually assumed that the imaginary part of the energy of a decaying resonance is (except a minus sign) half the width. Other examples are the interpretation of complex cross sections done by Berggren [3] or the widely used radioactive decay width evaluated by Thomas as the residues of the S-matrix [4]. All these interpretations are valid only if the resonances are isolated and, therefore, narrow. In this case the residues of the S-matrix becomes real. One may thus apply this theory and evaluate all resonances, giving physical meaning to the narrow ones only. To achieve this goal a representation consisting of bound states, Gamow resonances and the proper continuum was proposed some years ago [2] (Berggren representation). One chooses the proper continuum as a given contour in th...

A linear universal decay formula is presented starting from the microscopic mechanism of the charged-particle emission. It relates the half-lives of monopole radioactive decays with the Q values of the outgoing particles as well as the masses and charges of the nuclei involved in the decay. This relation is found to be a generalization of the Geiger-Nuttall law in alpha radioactivity and explains well all known cluster decays. Predictions on the most likely emissions of various clusters are presented.

The Hartree-Fock-Bogoliubov (HFB) equations in coordinate representation are solved exactly, i.e., with correct asymptotic boundary conditions for the continuous spectrum. The calculations are preformed with effective Skyrme interactions. The exact HFB solutions are compared with HFB calculations based on box boundary conditions and with resonant continuum Hartree-Fock-BCS (HF-BCS) results. The comparison is done for the neutron-rich Ni isotopes. It is shown that close to the drip line the amount of pairing correlations depends on how the continuum coupling is treated. On the other hand, the resonant continuum HF-BCS results are generally close to those of HFB even in neutron-rich nuclei.Comment: 9 figures, corrected ref.

A linear relation for charged-particle emissions is presented starting from the microscopic mechanism of the radioactive decay. It relates the logarithms of the decay half-lives with two variables, called χ ′ and ρ ′ , which depend upon the Q-values of the outgoing clusters as well as the masses and charges of the nuclei involved in the decay. This relation explains well all known cluster decays.It is found to be a generalization of the Geiger-Nuttall law in α radioactivity and therefore we call it the universal decay law. Predictions on the most likely emissions of various clusters are presented by applying the law over the whole nuclear chart. It is seen that the decays of heavier clusters with non-equal proton and neutron numbers are mostly located in the trans-lead region.The emissions of clusters with equal protons and neutrons, like 12 C and 16 O, are possible in some neutron-deficient nuclei with Z ≥ 54.